Exact scalar-tensor cosmological solutions via Noether symmetry

In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic energy, respectively. We also include the scalar field self-interaction potential into the gravitational action. From the condition of the vanishing of the Lie derivative of the gravitational cosmological Lagrangian with respect to a given vector field we obtain three cosmological solutions describing the time evolution of a spatially flat Friedman-Robertson-Walker Universe filled with a scalar field. The cosmological properties of the solutions are investigated in detail, and it is shown that they can describe a large variety of cosmological evolutions, including models that experience a smooth transition from a decelerating to an accelerating phase.